No-wait Flow Shop Scheduling Problem Research Articles

No-wait flow shop scheduling using fuzzy multi-objective linear programming

This study develops a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-objective no-wait flow shop scheduling problem in a fuzzy environment. The proposed model attempts to simultaneously minimize the weighted mean completion time and the weighted mean earliness. A numerical example demonstrates the feasibility of applying the proposed model to no-wait flow shop scheduling problem. The proposed model yields a compromised solution and the decision maker's overall levels of satisfaction.

A Heuristic Genetic Algorithm for No-Wait Flowshop Scheduling Problem

Abstract No-wait flowshop scheduling problems with the objective to minimize the total flow time is an important sequencing problem in the field of developing production plans and has a wide engineering background. Genetic algorithm (GA) has the capability of global convergence and has been proven effective to solve NP-hard combinatorial optimization problems, while simple heuristics have the advantage of fast local convergence and can be easily implemented. In order to avoid the defect of slow convergence or premature, a heuristic genetic algorithm is proposed by incorporating the simple heuristics and local search into the traditional genetic algorithm. In this hybridized algorithm, the structural information of no-wait flowshops and high-effective heuristics are incorporated to design a new method for generating initial generation and a new crossover operator. The computational results show the developed heuristic genetic algorithm is efficient and the quality of its solution has advantage over the best known algorithm. It is suitable for solving the large scale practical problems and lays a foundation for the application of meta-heuristic algorithms in industrial production.

An improved iterated greedy algorithm for the no-wait flow shop scheduling problem with makespan criterion

An improved iterated greedy algorithm (IIGA) is proposed in this paper to solve the no-wait flow shop scheduling problem with the objective to minimize the makespan. In the proposed IIGA, firstly, a speed-up method for the insert neighborhood is developed to evaluate the whole insert neighborhood of a single solution with (n − 1)2 neighbors in time O(n 2), where n is the number of jobs; secondly, an improved Nawaz-Enscore-Ham (NEH) heuristic is presented for constructing solutions in the initial stage and searching process; thirdly, a simple local search algorithm based on the speed-up method is incorporated into the iterated greedy algorithm to perform exploitation. The computational results based on some well-known benchmarks show that the proposed IIGA can obtain results better than those from some existing approaches in the literature.

A hybrid discrete particle swarm optimization algorithm for the no-wait flow shop scheduling problem with makespan criterion

This paper proposes a novel hybrid discrete particle swarm optimization (HDPSO) algorithm to solve the no-wait flow shop scheduling problems with the criterion to minimize the maximum completion time (makespan). Firstly, a simple approach is presented in the paper to calculate the makespan of a job permutation. Secondly, a speed-up method is proposed to evaluate the similar insert neighborhood solution. Thirdly, a discrete particle swarm optimization (DPSO) algorithm based on permutation representation and a local search algorithm based on the insert neighborhood are fused to enhance the searching ability and to balance the exploration and exploitation. Then, computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is concluded that the proposed HDPSO algorithm is superior to both the single DPSO algorithm and the existing hybrid particle swarm optimization (HPSO) algorithm from literature in terms of searching quality, robustness and efficiency.

A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: Weighted mean completion time and weighted mean tardiness

This paper investigates a novel multi-objective model for a no-wait flow shop scheduling problem that minimizes both the weighted mean completion time ( C ¯ w ) and weighted mean tardiness ( T ¯ w ) . Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new hybrid multi-objective algorithm based on the features of a biological immune system (IS) and bacterial optimization (BO) to find Pareto optimal solutions for the given problem. To validate the performance of the proposed hybrid multi-objective immune algorithm (HMOIA) in terms of solution quality and diversity level, various test problems are examined. Further, the efficiency of the proposed algorithm, based on various metrics, is compared against five prominent multi-objective evolutionary algorithms: PS-NC GA, NSGA-II, SPEA-II, MOIA, and MISA. Our computational results suggest that our proposed HMOIA outperforms the five foregoing algorithms, especially for large-sized problems.

The no-wait two-machine flow shop scheduling problem with convex resource-dependent processing times

We extend the classical no-wait two-machine flow shop scheduling problem to the case where job-processing times are controllable through the allocation of a common, limited and nonrenewable resource. Our objective is to simultaneously determine the sequence of the jobs and the resource allocation for each job on both machines in order to minimize the makespan. By using the equivalent load method to obtain the optimal resource allocation on a series-parallel graph, we reduce the problem to a sequencing one and show that it is equivalent to a new special case of the Traveling Salesman Problem (TSP). We prove that although the reduced problem forms a subclass of the TSP on permuted Monge matrices, it is still strongly NP-hard. We provide an approximation result and present three special cases which are polynomially solvable. We have also tested two different subtour-patching heuristics in large-scale computational experiments on randomly generated instances of the problem. Both heuristics produced close-to-optimal solutions in most cases.

Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm

Flow shop scheduling problems have gained wide attention both in practical and academic fields. In this paper, we consider a multi-objective no-wait flow shop scheduling problem by minimizing the weighted mean completion time and weighted mean tardiness simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in a strong sense, an effective immune algorithm (IA) is proposed for searching locally the Pareto-optimal frontier for the given problem. To validate the performance of the proposed algorithm in terms of solution quality and diversity level, various test problems are carried out and the efficiency of the proposed algorithm, based on some comparison metrics, is compared with a prominent multi-objective genetic algorithm, i.e., strength Pareto evolutionary algorithm II (SPEA-II). The computational results show that the proposed IA outperforms the above genetic algorithm, especially for large problems.

COMPARISON OF SCHEDULING EFFICIENCY IN TWO/THREE-MACHINE NO-WAIT FLOW SHOP PROBLEM USING SIMULATED ANNEALING AND GENETIC ALGORITHM

This paper considers two/three-machine no-wait flow shop scheduling problems with makespan minimization. Inherited with the NP-hard problem nature, this scheduling problem is solved by using a Simulated Annealing (SA) and Genetic Algorithm (GA) instead of mathematical programming. These two well-known search algorithms are often used to solve complex combinational optimization problems. In order to compare the performance of the two algorithms, we use solution quality (under the same computational time) and computation efficiency (under the same solution quality) as the measuring criteria. From the example problem, we found that SA is superior to GA in both solution quality and computation efficiency under identical terminating conditions. The performance of SA and GA decreased upon increasing the number of jobs. Our main contributions are to compare SA and GA under limited resources, which would be more consistent with the real world.

Flow shop scheduling problems with deteriorating jobs under dominating machines

This paper considers the general, no-wait and no-idle flow shop scheduling problems with deteriorating jobs. By a deteriorating job we mean that the processing time is an increasing function of its execution starting time. A linear deterioration function is assumed and some dominating relationships between machines can be satisfied. It is shown that for the problems to minimize the makespan or the weighted sum of completion time, polynomial algorithms still exist, although these problems are more complicated than the classical ones. When the objective is to minimize the maximum lateness, the solutions of a classical version may not hold.

Solvable Cases of the No-Wait Flow-Shop Scheduling Problem

The no-wait flow-shop scheduling problem (NWFSSP) with a makespan objective function is considered. As is well known, this problem is 𝒩𝒫-hard for three or more machines. Therefore, it is interesting to consider special cases, i.e. special structured processing time matrices, that allow polynomial time solution algorithms. Furthermore, it is well known that the NWFSSP with a makespan objective function can be formulated as a travelling salesman problem (TSP). It is observed that special structured processing time matrices for the NWFSSP lead to special structured distance matrices for which the TSP is polynomially solvable. Using this observation, it is shown that some NWFSSPs with fixed processing times on all except two machines are well solvable while the others are conjectured to be 𝒩𝒫-hard. Also, it is shown that NWFSSPs with a mean completion time objective function restricted to semi-ordered processing time matrices are easily solvable.